# RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots (Updated For 2021-22)

RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots: Be it your Class 8 Maths assignments or the tests, RS Aggarwal Solutions Class 8 Maths has got you covered. You can find credible and accurate solutions of RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots designed by the subject matter experts. All the solutions are designed as pe the current CBSE Syllabus.

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RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots

## RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots – Overview

• Definitions

The value generated by multiplying the number by itself is called the Square of a number.

The value that, when multiplied by itself, gives the original value, is the square root of a number.

For example:

(6)² = 36

Square of 6 is 36 whereas 6 is the square root of 36. Therefore, the concept of the square and square root are opposite.

• Properties Of A Square Number
1. Square of any number gives a positive number.
2. Square of 1 is 1.
3. Square of 0 is 0.
4. The Square of a number under the root gives the same number as the number under the root.
5. For example (√3)² = 3

There are 2 ways to find the square root of a number correctly:

1. Prime Factorisation Method
2. Using Long Division Method
• Squares and Square Roots of Numbers From 1 to 50

 Number Square of Number Square Root of Number 1 1 1.000 2 4 1.414 3 9 1.732 4 16 2.000 5 25 2.236 6 36 2.449 7 49 2.646 8 64 2.828 9 81 3.000 10 100 3.162 11 121 3.317 12 144 3.464 13 169 3.606 14 196 3.742 15 225 3.873 16 256 4.000 17 289 4.123 18 324 4.243 19 361 4.359 20 400 4.472 21 441 4.583 22 484 4.690 23 529 4.796 24 576 4.899 25 625 5.000 26 676 5.099 27 729 5.196 28 784 5.292 29 841 5.385 30 900 5.477 31 961 5.568 32 1,024 5.657 33 1,089 5.745 34 1,156 5.831 35 1,225 5.916 36 1,296 6.000 37 1,369 6.083 38 1,444 6.164 39 1,521 6.245 40 1,600 6.325 41 1,681 6.403 42 1,764 6.481 43 1,849 6.557 44 1,936 6.633 45 2,025 6.708 46 2,116 6.782 47 2,209 6.856 48 2,304 6.928 49 2,401 7.000 50 2,500 7.071
• Perfect and Imperfect Square
1. Perfect Square: If a whole number is multiplied by itself to generate a given number, it is said to be a Perfect square.

Example:

25−−√=5×5−−−−√=5
2. Imperfect square: If a whole number is not multiplied to generate a given number, it is an imperfect square.

Example:

13−−√=3.606
• In between Squares

Suppose the 2 consecutive squares are n² and (n+1)², then the number between them is 2n.

For example:

Find the numbers between 2² and 3².

2² = 4

3² = 9

And, n = 2

Therefore, the total numbers between 4 and 9 = 2n = 4

Therefore, the numbers are 5, 6, 7, 8.

• Pythagorean Triplet

3 positive integers a, b, c which satisfies this Pythagoras theorem a²+b²=c² is called the Pythagorean Triplet and the positive integers are called Pythagorean triples.

Example: (3, 4, 5)

By evaluating we get:

32 + 42 = 52

9 + 16 = 25

Hence, 3, 4, and 5 are the Pythagorean triples.

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